The geodesic flow of a generic metric does not admit nontrivial integrals polynomial in momenta

DOI10.1088/0951-7715/29/6/1755zbMath1350.37064arXiv1510.01493OpenAlexW2219591152MaRDI QIDQ2813863

Vladimir S. Matveev, Boris S. Kruglikov

Publication date: 27 June 2016

Published in: Nonlinearity (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1510.01493

zbMATH Keywords

geodesic flowsKilling tensorsfinite-dimensional integrable systemspolynomial in momenta integrals

Mathematics Subject Classification ID

Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests (37J35) Completely integrable systems and methods of integration for problems in Hamiltonian and Lagrangian mechanics (70H06) Geodesic flows in symplectic geometry and contact geometry (53D25) Nonintegrable systems for problems in Hamiltonian and Lagrangian mechanics (70H07) Obstructions to integrability for finite-dimensional Hamiltonian and Lagrangian systems (nonintegrability criteria) (37J30)

Related Items (13)

Quantum integrability for the Beltrami-Laplace operators of projectively equivalent metrics of arbitrary signatures ⋮ Killing tensors in Koutras–Mcintosh spacetimes ⋮ Integrable Geodesic Flows ⋮ On integrability of the Killing equation ⋮ Killing tensors in stationary and axially symmetric space-times ⋮ Integrable cosmological potentials ⋮ On integrability of certain rank 2 sub-Riemannian structures ⋮ On the geometric and analytical properties of the anharmonic oscillator ⋮ Geometry of solutions to the c-projective metrizability equation ⋮ Open problems, questions and challenges in finite- dimensional integrable systems ⋮ Metrics in projective differential geometry: the geometry of solutions to the metrizability equation ⋮ On projective and affine equivalence of sub-Riemannian metrics ⋮ Open problems and questions about geodesics

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